Ring-Planet
Planetary transmission made of drive, ring and planetary gears with adjustable gear ratio and friction losses.
Description
The Ring-Planet unit is a drive gear, ring gear and a set of planetary gears. The planetary gears mesh with the drive gear and rotate with it. The planetary and ring gears rotate at a fixed gear ratio that you specify. The ring-planetary gear and sun-planetary gear are the basic elements of a planetary gearbox.
Thermal model
You can model the effects of heat flow and temperature change by enabling the optional thermal port. To use the thermal port, set the Friction model parameter to `Temperature-dependent efficiency'.
Equations
Ideal gears and gear ratios
The Ring-Planet block imposes one kinematic and one geometric constraint on three linked axes:
The gear ratio for ring gear and planetary gear meshing is equal to:
where is the number of teeth on each gear. In terms of this relationship, the key kinematic constraint is:
The three degrees of freedom are reduced to two independent pairs of gears: .
| The gear ratio of the planetary gear must be . |
Torque transmission is carried out as follows:
In the ideal case where there are no torque transmission losses, .
Non-ideal limits and losses in gears
In the non-ideal case, . For more details, see Modelling of mechanical gears with losses.
Ports
Conserving
#
С
—
drive pinion
`rotational mechanics
Details
A non-directional port associated with the drive gear.
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#
P
—
planetary gear
`rotational mechanics
Details
A non-directional port associated with a planetary gear.
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#
R
—
ring gear
`rotational mechanics
Details
A non-directional port associated with a ring gear.
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#
H
—
heat flux
`heat
Details
A non-directional port associated with heat flow.
The heat port allows modelling the heat flow between the unit and the connected network.
Dependencies
To use this port, set Friction model to `Temperature-dependent efficiency'.
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Parameters
Main
# Ring (R) to planet (P) teeth ratio (NR/NP) — gear ratio from ring gear to planetary gear
Details
Constant gear ratio, , ring gear revolutions to planetary gear revolutions. Determined by the number of teeth of the ring gear divided by the number of teeth of the planetary gear. The gear ratio must be >1.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
Meshing Losses
#
Friction model —
friction model
No meshing losses - Suitable for HIL simulation | Constant efficiency | Temperature-dependent efficiency
Details
A model of friction in a transmission. Defined as:
-
No meshing losses - Suitable for HIL simulation- the gearing is assumed to be perfect. -
Constant efficiency- torque transmission between gear pairs is reduced by a constant efficiency value, , so that . -
Temperature-dependent efficiency- the torque transmission between gear pairs is determined by an interpolation table of temperature and torque transmission efficiency.
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| Evaluatable |
No |
# Ordinary efficiency — Torque transmission efficiency
Details
Torque transmission efficiency, , for meshing the outer and inner pair of planetary gears. This value must be in the range (0,1].
Dependencies
To use this parameter, set Friction model to Constant efficiency.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Temperature —
vector of temperature values
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
A vector of temperature values used to construct an interpolation table of temperature and torque transmission efficiency. The elements of the vector should be monotonically increasing.
Dependencies
To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.
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| Evaluatable |
Yes |
# Efficiency — vector of efficiency values
Details
Vector of efficiency values, , for ring gear and planetary gear.
The unit uses these values to build an interpolation table of temperature and efficiency correspondence.
Each element is an efficiency related to the temperature vector of the Temperature parameter. The length of the vector must be equal to the length of the vector of the Temperature parameter. Each element of the vector must be in the range (0,1].
Dependencies
To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Planet-carrier power threshold —
minimum threshold power value
W | GW | MW | kW | mW | uW | HP_DIN
Details
The threshold power value above which the full efficiency value is applied. Below this value, the efficiency value is smoothed using a hyperbolic tangent function.
-
If Friction model is set to `Constant efficiency', the unit reduces losses to zero when no power is transmitted.
-
If Friction model is set to `Temperature-dependent efficiency', the unit smooths the efficiencies between zero at rest and the values given in the interpolation tables for temperature and torque transfer efficiency.
Dependencies
To use this parameter, set the Friction model parameter to `Constant efficiency' or `Temperature-dependent efficiency'.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
Viscous Losses
#
Planet-carrier viscous friction coefficient —
viscous friction coefficient between gears
N*m*s/rad | ft*lbf*s/rad
Details
Viscous friction coefficient for the movement of the planetary and carrier gears.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
Thermal Port
#
Thermal mass —
heat capacity
J/K | kJ/K
Details
The heat energy required to change the temperature of a component by one degree. The greater the heat capacity, the more resistant the component is to temperature change.
Dependencies
To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |